Mathematics teachers must expect reasonably high standards of achievement from pupils. Too frequently, pupils attain at a substandard level and more optimal achievement is necessary. Thus, pupils should have self esteem needs met in the school and classroom setting. Thus, learners feel that mathematics is worthwhile and effort must be put forth to accomplish and grow to achieve objectives. With the common core objectives and tests, teachers need to align the subject matter taught with the proposed ends of instruction. Each pupil needs to have help, as necessary, from the teacher as well as from peers to achieve objectives, in the common core. A collaborative environment must be in the offing so that pupils feel confident of trust and empathy being in the offing (Ediger and Rao, 2011).
The Common Core
The teacher should have high expectations for learner progress in mathematics. These expectations must be reasonable. Pupils can be aided to attain at a higher level with scaffolding. Here, the math teacher notices the present achievement level of each pupil and when difficulties arise, assists the learners with intermediate explanations to move from the present to a bar set upward. Knowledgeable and skillful teachers are able to do this to realize more optimal pupil achievement. With getting to know each pupil's level of attainment, the teacher might well be able to secure an upward level of progress with quality instruction, and this includes scaffolding. The focal point is upon the child and his/her present status in mathematics and through scaffolding realize an optimal level (National Council Teachers of Mathematics, 2000).
Effort, not native ability and aptitude, is salient to consider in teaching. The writer has heard children state that "Mathematics is just not my cup of tea, and my parents were the same way." Here, the problem is justification for lower achievement and a lack of effort put forth to reach out and attain vital objectives. Jerome Bruner wrote, "Any subject matter can be learned in some intellectually honest form by an child at any stage of development." The concern here is "in some intellectually honest form," indicating that it must harmonize with the learner's present level of attainment before moving on to more complex key facts, concepts, and generalizations. The structure of mathematics is then a focal point of teaching, not trivia nor the irrelevant. Mathematics can also be highly practical as well as utilitarian for pupils (See NCTM 2003).
Positive attitudes must be infused in pupil thinking in that he/she can do mathematics well. Learners then need to experience success in learning. They need to be able to explain a new process acquired in their very own words; the teacher might then diagnose misunderstandings and that which needs further elaboration. Formative assessments given during the time a unit is taught also provides feedback in terms of what is lacking in mastery learning. A good teacher is a reputable diagnostician (Ediger, 1989).
Providing for diverse styles of learning is salient. By doing this, pupils have better opportunities to achieve objectives in mathematics and in the common core. The following are some of the considerations in emphasizing learning styles:
* working by the self or doing assignments collectively in committees
* inductive versus deductive activities
* heavy use of teacher explanations versus constructivism
* cognitive objectives stressed solely, as compared to affective/attitudinal goals in the mathematics curriculum
* teachers sequencing pupil progress in mathematics versus rather heavy learner involvement in ascertaining order of experiences
* carefully selected textbook use in determining the math curriculum as compared to heavy infusion of problem solving experiences (Ediger, 2006).
The common core test results then may be upped by teachers paying careful attention to individual leaning styles. …